Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

TL;DR

This paper reviews invariants of algebraic singularities over perfect fields and demonstrates how they facilitate a synthetic proof of embedded resolution of singularities for 2-dimensional schemes.

Contribution

It introduces a new approach using invariants to provide a synthetic proof of resolution of singularities in two dimensions.

Findings

Invariants effectively characterize algebraic singularities.

Synthetic proof simplifies the resolution process.

Resolution method applies to 2-dimensional schemes.

Abstract

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.